"ליצחק ושבועתו אברהם את כרת אשר"
This passuk, whose source is in Divrei Hayamim (I, 16:16), is brought in Sefer Tehillim (105:9) with a slight variation: Instead of "ushvu’aso leYitzchak," it says "ushvu’aso leYischak."
The Imrei Emes explained the meaning of the name "ישחק": Even before Yitzchak’s birth, HaKadosh Baruch Hu instructed Avraham (Bereishis 17:19): "But Sarah your wife will bear for you a son and you will name him Yitzchak," in the name of the tzechok, the laughter that Avraham laughed when he was told about the son that would be born to him (Rashi ibid). Right upon the birth of his son, Avraham hastened to fulfill the commandment of Hashem, and called his son Yitzchak. But when he made the bris, because he wanted to call him a name in the custom of Am Yisrael, he gave him another name expressing that same laughter: "Yischak."
That is the reason that in the order of the pesukim said at the bris milah, after the brachos, we use specifically the passuk in Tehillim, "Ushvua’so leYischak," because as noted, this was the name given to Yitzchak when he was brought into the covenant of Avraham Avinu.
Imrei Emes, Likutim p. 94
